Modified Lee-Carter model using extreme value theory for forecasting mortality rates amidst extreme events during COVID-19 era in Indonesia

Abstract

In recent years, the world has been grappling with the threat of pandemics, as well as conflicts and wars between countries. Events such as pandemics and conflicts are extreme conditions that can arise unexpectedly, causing significant casualties. Consequently, there is a need for modeling that can account for mortality resulting from these extreme events. The Lee-Carter model utilizes mortality rate data from observed age groups over time. To address extreme mortality rates, the Lee-Carter model has been adapted using Extreme Value Theory (EVT), resulting in the modified Lee-Carter EVT Model. The EVT approach employed is the Peak Over Threshold (POT) approach with Generalized Pareto Distribution (GPD). This model was applied to Indonesian mortality rate data from 1998 to 2020 to forecast mortality rates for the Covid-19 pandemic period in 2021 and 2022. In GPD modeling, a threshold value of 0.02 is determined. Values exceeding the threshold are modeled with GPD, while values below the threshold are modeled with normal and empirical distribution. The results, assessed using Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE), indicate that the Extreme Value Theory Modified Lee-Carter empirical distribution model yields the smallest MAPE value at 12.156%. In comparison, the Extreme Value Theory Modified Lee-Carter normal distribution model has a MAPE value of 13.175%, and the regular Lee-Carter model is at 13.343%. These findings pertain to predicting Indonesia’s mortality rate in age groups experiencing extreme events.